Q&A

 Master

Pumping the accelerator pedal on a fuel injected Honda isn't doing anything beneficial to make the car start. Old carburetor cars pumping the pedal squirted gas into the engine if the choke wasn't working and made the mixture richer enabling the car to start.
If the car won't crank over check battery connections are clean and secure. The ignition switch electrical portion often fails.
If the vehicle cranks over but doesn't start the fuel pump relay/main relay under the dash on the left side fails.
I would try to diagnose the problem by putting a fuel pressure gauge and verify fuel pressure when the car won't start, and a timing light on the plug wire to verify spark at the plugs.
If you are missing fuel or spark you need to look at a wiring diagram and start looking at electrical power, grounds and signals.

check the main relay that relay controls the fuel pump